Within the context of developing complex network theories and a netcentric approach, this paper introduces a new concept that describes the elements of interaction of complex network systems, including comprehensive network lace (supercomplex networks), with its intrinsic multilayered thematic and dynamic nature. It emphasizes inter-penetrative competitive and cooperative relationships of thematic layers. Contemporary interpretations of supercomplex networks instantiated by biologic, social, and economic systems have been considered. The new concept will give a basis for developing instruments for effective management, governance, and support of state regulation processes in countering global disasters.